JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 117, A12310, doi:10.1029/2012JA018140, 2012
ELF/VLF wave generation from the beating of two HF ionospheric
heating sources
M. B. Cohen,1 R. C. Moore,2 M. Golkowski,3 and N. G. Lehtinen1
Received 19 July 2012; revised 28 September 2012; accepted 24 October 2012; published 13 December 2012.
[1] It is well established that Extremely Low Frequency (ELF, 0.3–3 kHz) and Very
Low Frequency (VLF, 3–30 kHz) radio waves can be generated via modulated High
Frequency (HF, 3–10 MHz) heating of the lower ionosphere (60–100 km). The ionospheric
absorption of HF power modifies the conductivity of the lower ionosphere, which in the
presence of natural currents such as the auroral electrojet, creates an ‘antenna in the sky.’
We utilize a theoretical model of the HF to ELF/VLF conversion and the ELF/VLF
propagation, and calculate the amplitudes of the generated ELF/VLF waves when two HF
heating waves, separated by the ELF/VLF frequency, are transmitted from two adjacent
locations. The resulting ELF/VLF radiation pattern exhibits a strong directional dependence
(as much as 15 dB) that depends on the physical spacing of the two HF sources. This beat
wave source can produce signals 10–20 dB stronger than those generated using amplitude
modulation, particularly for frequencies greater than 5–10 kHz. We evaluate recent
suggestions that beating two HF waves generates ELF/VLF waves in the F-region
(>150 km), and conclude that those experimental results may have misinterpreted,
and can be explained strictly by the much more well established D region mechanism.
Citation: Cohen, M. B., R. C. Moore, M. Golkowski, and N. G. Lehtinen (2012), ELF/VLF wave generation from the beating of
two HF ionospheric heating sources, J. Geophys. Res., 117, A12310, doi:10.1029/2012JA018140.
1. Introduction
[2] Extremely Low Frequency (ELF, 0.3–3 kHz) and Very
Low Frequency (VLF, 3–30 kHz) radio waves are difficult to
generate with conventional antennas, due primarily to their
long wavelengths (10–1000 km). On the other hand, ELF/VLF
waves have broad applications to ionospheric and magnetospheric remote sensing, and long distance communications. A
practically realizable and permanent vertical antenna is much
shorter than a wavelength and thus can radiate reasonable
ELF/VLF power only after being tuned to a narrow frequency
band [Watt, 1967]. On the other hand, the ELF/VLF radiation
from a horizontal antenna will suffer from the image current
just beneath the conducting ground which cancels out the
power radiated by the antenna.
[3] Recent decades have seen new research into creating
an ‘antenna in the sky’, to overcome the limitations of practical ELF/VLF transmitter design. The first observations by
Getmantsev et al. [1974] in the USSR were followed by a
1
Department of Electrical Engineering, Stanford University, Stanford,
California, USA.
2
Department of Electrical Engineering, University of Florida,
Gainesville, Florida, USA.
3
Department of Electrical Engineering, University of Colorado Denver,
Denver, Colorado, USA.
Corresponding author: M. B. Cohen, Department of Electrical
Engineering, Stanford University, 350 Serra Mall, Rm. 356, Stanford, CA
94305, USA. ([email protected])
©2012. American Geophysical Union. All Rights Reserved.
0148-0227/12/2012JA018140
long series of experiments at Tromsø Norway [Stubbe et al.,
1981; Barr and Stubbe, 1984; Rietveld et al., 1984, 1987;
Barr et al., 1987; Barr and Stubbe, 1991, 1997; Barr, 1998],
and later at the High Frequency Active Auroral Research
Program (HAARP) facility near Gakona, Alaska, which was
upgraded in 2007 to 3.6 MW of power [Cohen et al., 2008a;
Golkowski et al., 2008, 2011; Cohen et al., 2011; Moore and
Agrawal, 2011; Fujimaru and Moore, 2011]. Using a High
Frequency (HF, 3–30 MHz) transmitter on the ground, the
free ionospheric electrons in the lower ionosphere are heated,
thus changing the conductivity of the ionosphere. The lower
ionosphere as defined here includes 60–100 km altitude, and
is referred to here as the D region although it also includes the
lowest part of the E region (85–100 km). In the presence of
natural currents such as the auroral electrojet, periodic modulation of the HF heating imposes the same modulation on
the electrojet currents, thus radiating the modulation frequency (as well as at its harmonics). HF heaters have been
built in Russia, Norway, Alaska, and Puerto Rico, and consist
of a grid of antennas capable of focusing HF energy into a
narrow upward beam, with effective radiated powers as high
as the GW range.
[4] Although the generated signals have been detected as
far as 4400 km away [Moore et al., 2007; Cohen et al.,
2010c], two key limitations of this scheme remain before
it could possibly be used as a practical communications system: (1) the efficiency remains quite low, on the order of
0.001% [Moore et al., 2007], and (2) the generation
mechanism requires the presence of natural ionospheric
currents, greatly constraining the feasible locations and
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limiting the reliability (an equatorial electrojet HF heating
facility has not yet been constructed, although a powerful
VHF radar at Jicamarca, Peru, did generate a weak 2.5 kHz
signal when modulated [Lunnen et al., 1984]). The first
limitation has been mitigated by a recent advance that utilizes
beam steering rather than square wave amplitude modulation
that delivers 10 dB more ELF/VLF power than vertical AM
heating [Cohen et al., 2008b, 2010b], although further
increases in efficiency are needed. Recent suggestions to use
dual beam ionospheric heating [Moore and Agrawal, 2011]
and time of arrival analysis [Fujimaru and Moore, 2011] may
lead to additional efficiency improvements.
[5] One proposed technique to circumvent the need for an
electrojet is to attempt to generate waves in the F region.
Presently, at least two approaches to F region generation have
been investigated experimentally. Papadopoulos et al. [2011]
described driving pressure gradients in the F region to form
magneto-sonic waves, which then convert to Hall currents in
the E region. The second proposed method involves broadcasting two continuous HF waves from the ground separated
by a ELF/VLF frequency [Kuo et al., 2011, 2012]. We discuss
here the second of these two methods.
[6] A prominent pioneering work on the beating of two HF
sources for wave generation is that of Barr and Stubbe
[1997], using the Tromsø heating facility. The six rows of
an antenna grid were divided into two halves, each with three
rows. One half was driven with a continuous 4.04 MHz input,
and the other with a frequency higher by the desired ELF/
VLF generation frequency. Hardware limitations prevented a
large frequency separation, but for the two frequencies tested
(565 Hz and 2006 Hz), the signals observed 500 km to the
south were substantially weaker (11 dB) from the beat wave
technique compared to the a square wave technique in which
the HF power is keyed on and off. However, Barr and Stubbe
[1997] then describe a simplified model of the wave generation (assuming a D region source), which matched experimental results, and then used the theory to predict that the
beat wave approach would produce higher amplitudes on the
ground at higher frequencies than they were able to test.
Villaseñor et al. [1996] also compare a beat wave approach
(referred to therein as DF) with amplitude modulation using
the High-Power Auroral Stimulation (HIPAS) facility in
Alaska, and present evidence for a common source height
based on wave polarizations as a function of frequency, and
confirm that the DF technique can produce stronger amplitudes above 5 kHz.
[7] Kuo et al. [2011] describe a physical process by which
the same beat wave technique could produce a source of
waves in the F-region via an electrojet-independent mechanism, under proper geomagnetic conditions (low D region
absorption) and choice of HF frequency. Using the HAARP
facility, Kuo et al. [2011] cite a case where magnetometer
activity was weak, and yet generation of ELF/VLF waves
via beat wave was observed to occur. Recent work by Jin
et al. [2011], however, shows that a weak magnetometer
reading does not imply that there will be no generation. Kuo
et al. [2012] then provided a comparison between the beat
wave and amplitude modulation techniques, showing that
the former can be stronger. On the other hand, Moore et al.
[2012] used an observational time of arrival technique in
conjunction with a beat wave experiment to show that the
source region was in the D region, not the F region.
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[8] In this work, we evaluate theoretically the generation
of ELF/VLF waves via beat waves from two closely spaced
(i.e., on the order of wavelengths) HF sources heating the
D region, and find substantial enhancement of wave generation compared to sinusoidal power modulation. The resulting directional dependence is also similar to the geometric
modulation techniques [Cohen et al., 2008b, 2010b]. In
particular, the separation of the two HF sources on the ground
create a phasing effect in the D region of the ionosphere
which changes the spatial distribution of ELF/VLF signals on
the ground. We find that the experimental results of both
Kuo et al. [2011] and Kuo et al. [2012] can be explained
using only a D region source. We note that these results are
consistent with the original findings presented by Barr and
Stubbe [1997], although the model presented herein is more
complete. Furthermore, we extend the conclusion to a different modulation waveform for which the voltage envelope
to the antenna array is modulated as the square root of a sine
wave, so that the HF power radiated is modulated sinusoidally, identical to the technique utilized by Kuo et al. [2012].
We will refer to this modulation as sinusoidal power modulation. It is worth noting that square wave amplitude modulation, as used by Barr and Stubbe [1997], typically produces
1–3 dB stronger signals than sinusoidal power modulation.
onger signals).
2. Model Description
[9] We utilize a pair of three-dimensional models which
together simulate the HF to ELF/VLF conversion and propagation process, described by Cohen et al. [2010a]. The HF
heating model is based on earlier work [Tomko, 1981;
Rodriguez, 1994; Moore, 2007; Payne et al., 2007]. The
model solves an energy balance equation that includes collisional heating and cooling, and assumes a Maxwellian electron energy distribution as described by page 165 of
Bittencourt [2003].
3
dTe
Ne kB
¼ 2kcS Le ðTe ; T0 Þ
2
dt
ð1Þ
where Te is the heated electron temperature, Ne is the electron
density, kB is Boltzmann’s constant, k is the wave number, c
is the imaginary (absorbing) part of the refractive index calculated from the Appleton-Hartree equation, S is the HF
power density, and Le is a sum of electron loss terms, each a
function of Te and the ambient electron temperature (T0).
[10] The electron loss rates are documented by pages 175–
178 of Rodriguez [1994], with the elastic loss rates given by
Banks [1966], the rotational excitation loss rates given by
Mentzoni and Row [1963] and Dalgarno et al. [1968], and
the vibrational excitation loss rates given by Stubbe and
Varnum [1972]. The modified electron temperature modifies the collision frequency as discussed by page 176 of
Rodriguez [1994]. An effective collision frequency of 53n, as
discussed by Sen and Wyller [1960], is used to calculate the
Hall and Pedersen conductivity according to page 137 of
Tomko [1981], assuming a constant electrojet electric field.
HF refraction and wave normal angle bending are also taken
into account as described by chapter 2 of Moore [2007].
[11] The electron-neutral collision frequency and electron
temperature are evolved in time, in a three dimensional
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Figure 1. The HF heating pattern from the northward beat wave experiment, at 4.1 MHz, over a horizontal slice reaching 60 km altitude centered above HAARP. The pattern is shown at 10 different times in the
ELF/VLF cycle, indicated by the labels in the top left corner of each panel.
space. From these, the model calculates the Hall and Pedersen ionospheric conductivity magnitudes, and extracts the
amplitude and phase of the first harmonic. The ionospheric
electron density is assumed based on the IRI model for a high
latitude summer nighttime. The electron density is assumed
to not be affected by the HF heating process, since the energy
density is too low to ionize in the lower ionosphere, and the
electron density changes from slower chemical changes take
many minutes to take effect [Milikh and Papadopoulos,
2007]. The geomagnetic field is taken from the IGRF
model for 2011. The field line at HAARP has declination
22 and dip angle 16 .
[12] The amplitudes and phases of the conductivity changes yield current sources, with the electrojet-induced electric
field assumed to be 10 mV/m (consistent with Cohen et al.
[2010a]). These current sources, embedded in the ionosphere and spatially distributed, are fed as input into a full
wave model of ELF/VLF wave propagation [Lehtinen and
Inan, 2008, 2009]. The propagation model yields the electric and magnetic field values in and below the ionosphere. In
this paper, we focus on the predicted amplitudes received on
the ground.
[13] The HF heating model takes as input the power density as a function of time in a two-dimensional slab at the
bottom of the ionosphere, in this case 60 km altitude. The
power density is calculated by summing the phasor contributions of the two sources assuming free space propagation. The two phasors add constructively, then destructively,
alternating at the difference frequency, producing power
modulation at the difference frequency at each given location. Because the spacing of the two HF sources is significant
compared to a wavelength, the phase of the power modulation at each point is a strong function of space. From 60 km
upward, the HF energy is then propagated through the ionosphere taking into account absorption. The time steps utilized are 1 ms, short enough that the energy balance equation
can be linearized. In this case, the HF power input from
HAARP is assumed to come from two HF sources, representing two halves of the array. The entire array is 12 rows,
with 24.4 m between them, so the two half-grid sources are
assumed to be 146.3 m apart, or six rows.
[14] For the amplitude modulation simulations, the voltage
envelope to the antenna array is modulated as the square root
of a sine wave, so that the HF power radiated is modulated
sinusoidally, identical to the technique utilized by Kuo et al.
[2012].
3. Results
[15] The realistic radiation pattern of each half-grid is taken
as input into the model, based on measurements at the HAARP
array, including a main lobe and a series of smaller sidelobes
(at least 10 dB lower peak power density) stratified to the north,
south, east, and west along the grid of the HAARP array. The
two sources (one for each half of the grid) are separated by a
difference frequency, and the HF power into the D region of the
ionosphere results from the interference of these two sources as
a function of time.
[16] Figure 1 shows an example of the HF power input
resulting from the split-array beat-wave technique at 4.1 MHz.
The spatial distribution changes periodically, at the ELF/VLF
separation frequency. One may consider this situation as if the
two HF sources are offset in phase by an amount that changes
in time, and wraps around 360 every ELF/VLF period, and
separated by 146.3 m (almost precisely two HF wavelengths at
4.1 MHz). The 10 panels show the HF power density at ten
points in the ELF/VLF period, as a function of space, for an
80 km 80 km box centered at 60 km altitude and directly
above HAARP, oriented to geographic north and south. In the
top left panel, at the beginning of the ELF/VLF period, the two
HF sources are in phase, so that their power adds constructively directly above HAARP. The secondary power regions,
10–15 dB less in power, result from the sidelobes, which also
constructively interfere between the two sources. Because
the HAARP array is aligned 14 east of geographic north, the
sidelobes are also oriented along an axis in this direction. The
two HF sources are separated in this direction. For the rest of
this paper, the term ‘north’ with respect to HAARP refers to
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Figure 2. The calculated magnetic field amplitude on the ground (total horizontal component) for
amplitude modulation with a sinusoidal power envelope. The 12 panels each reflect the a 500 km 500 km box around HAARP, and the 12 panels represent 12 different frequencies, labeled in the
top left corner of each panel.
14 east of north, or along the direction of HAARPs northward
column. The ERP of HAARP at 4.1 MHz is 1.16 GW,
so that the maximum power density at 60 km altitude is
26 mW/m2. In these simulations, we use X-mode polarization, although the HF radiation pattern would not be different
for O-mode or linear polarization.
[17] The HF beam pattern can be interpreted as exhibiting
substantial motion in time, as earlier noted by Kotik et al.
[1986], Rapoport et al. [1994], and Barr and Stubbe [1997],
and in a similar manner to the ‘sawtooth sweep’ described by
Cohen et al. [2008b], in which the HF power is left on continuously, and a thin beam is swept in a linear direction (then
starting over from the other end), repeating every ELF/VLF
period. In the case shown in Figure 1, the more northward of
the two HF sources is lower in HF frequency, so that after 10%
of the ELF/VLF cycle, its phase lags the southward HF source
by 36 . Hence, the point of constructive interference between
the two sources is shifted to the north (as are the sidelobes). As
the ELF/VLF period progresses, reflected by the labels in the
upper left corner of each panel, the center of the HF heating
beam continues to shift northward, along with the southward
sidelobe which also moves along with the main beam while
gaining peak power. At the midway point, reflected in the
bottom left panel, the two HF sources are 180 out of phase,
resulting in destructive interference directly above HAARP.
From that point, what had been the main beam begins to lose
power and become a sidelobe, whereas the southward side
lobe moves northward and becomes the main lobe. The time
progression involves the entire interference pattern moving
northward, appearing on the southern edge of the slab, and
disappearing on the northern edge. We emphasize that this
figure shows the HF power, not the ELF/VLF power, and
there is no overall north/south disparity in the total power
density injected into the ionosphere. Any north/south disparity in the ELF/VLF generated pattern on the ground
therefore results from either the phasing of the HF power, or
the anisotropy of the HF heating and cooling process.
[18] For the case shown in Figure 1, the northward HF
source is lower in frequency, and the interference pattern
moves northward. On the other hand, if the southward HF
source were lower in frequency, the interference pattern
moves southward. As such, we distinguish two types of beat
wave techniques, in which the HF interference pattern can
move to the north, or to the south, due to the spatial separation of the two HF sources. On the other hand, traditional
amplitude modulation can be thought of as resulting from a
single source. For amplitude modulation, the pattern looks
like the top left panel of Figure 1, and the power simply
modulates as a sinusoid in time, with no spatial motion.
[19] Figure 2 shows the calculated magnetic field on the
ground for amplitude modulation, over a 250 km 250 km
box centered at HAARP. The power is assumed to be modulated sinusoidally in time. The propagation model yields all
three components of the magnetic field, and the plotted value
is the sum in quadrature of the two horizontal magnetic field
components (the vertical component is negligible because of
the high conductivity of the ground, and it is typically not
recorded in ELF/VLF ground measurements). The 12 panels
represent 12 different ELF/VLF frequencies, ranging from
1 kHz to 21.5 kHz, labeled in the top left corner of each panel.
These correspond to the same 12 frequencies that were part of
the experiment described by Kuo et al. [2012] that compared
amplitude modulation to beat wave. The radiation pattern
from sinusoidal power modulation is mostly isotropic around
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Figure 3. Same calculations as in Figure 2, except applied to the northward beat wave, where the northern half of HAARP operated at the lower HF frequency, and the HF radiation pattern thus moves
northward.
HAARP. There is some feature (most noticeable at 2 kHz)
that looks like a spiral pattern, resulting from the non-vertical
component of the geomagnetic field, and the asymmetric
response of the Hall and Pedersen conductivity, described
in Figure 3 of Cohen et al. [2010a]. Also evident is the
interference pattern of multimode ELF/VLF propagation,
appearing as concentric rings around HAARP, particularly at
the higher frequencies where more modes propagate, and the
free space wavelength is shorter.
[20] Figures 3 and 4 show the calculated magnetic field for
the northward and southward beat wave, with identical panels,
and at the same set of 12 frequencies. The radiation pattern on
the ground looks substantially different than the amplitude
modulation results at all frequencies. The northward and
southward beat wave radiation patterns also look essentially
the same, but the directional dependence is reversed by 180 .
[21] A key effect in the directional pattern is the apparent
physical horizontal speed of the HF heating pattern that
enters the ionosphere. As the frequency of the beat wave
separation increases, the HF power pattern moves to the north
or south increasingly fast. As the speed of the beam approaches the phase velocity of propagating waves in the Earthionosphere waveguide, there is a traveling wave tube effect
which acts to direct the radiation in a certain direction due to
the matched propagation between the phase fronts of the
generating ionospheric currents, and the phase fronts of the
generated ELF/VLF wave. This effect is similar to the geometric modulation ‘sawtooth sweep’. The HF radiation pattern moves horizontally at close to the speed of light at
8 kHz [Cohen et al., 2010b].
[22] Comparing Figures 3 and 4, this directional phasing
effect is exhibited as a pronounced increase in radiated
power in a northward (or southward) direction, observed
most prominently between 3.5 and 9.5 kHz. Below 3.5 kHz,
the motion is too slow, which limits the directional dependence of the radiation. Above 9.5 kHz, the HF radiation
pattern moves faster than the speed of light, although nothing is carried faster than the speed of light, but rather the
phase velocity of the interference pattern is faster than the
speed of light. In addition to the directional phasing effect,
some of the directional dependence arises from the asymmetric shape of the HF beam when it is comprised of a halfarray, similar to the broadened east-west beam described by
Cohen et al. [2012].
[23] Figure 5 shows the ratio of the ground magnetic field of
northward beat wave to the ground magnetic field of amplitude modulation, on a logarithmic scale. Red areas indicate
where the northward beat wave produces higher amplitude,
blue indicates where amplitude modulation produces higher
amplitude, white indicates similar magnetic field. There is a
clear trend that with increasing frequency, the beat wave
technique produces stronger magnetic fields compared to
amplitude modulation. At 1 and 2 kHz, amplitude modulation
produces stronger magnetic fields. At 3.5 kHz, northward
beat wave is stronger to the north of HAARP, but amplitude
modulation is stronger to the south of HAARP. Starting at
5.5 kHz, beat wave generation becomes increasingly advantageous compared to amplitude modulation, even in the
southward direction from HAARP. Although not shown, a
similar plot of the ratio of southward beat wave to amplitude
modulation looks almost identical to Figure 5, except that the
vertical axis is flipped. As noted earlier, square-wave amplitude modulation would produce ELF/VLF amplitudes that
are 1–3 dB stronger than those produced using sinusoidal
power modulation. An analysis using square-wave amplitude
modulation would yield similar results as shown in Figure 5,
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Figure 4. Same calculations as in Figure 2, except applied to the southward beat wave, where the southern
half of HAARP operated at the lower HF frequency, and the HF radiation pattern thus moves southward.
except that the frequency at which beat-wave modulation
becomes more efficient would be slightly higher.
[24] Figure 6 shows the calculated magnetic field at three
locations, at HAARP (Figure 6, left), 150 km northward of
HAARP (Figure 6, middle), and 150 km eastward of HAARP
(Figure 6, right). As in the previous descriptions, ‘north’
refers to the direction along HAARPs north-south axis,
which is 14 east of geographic north, and 8 west of geomagnetic north at HAARP. At HAARP, amplitude modulation has a frequency content that steadily decreases with
increasing frequency beyond 2 kHz, although there is some
deviation from a straight line due to resonances in the Earth-
Figure 5. The ratio of the magnetic field on the ground from the northward beat wave, to that of amplitude modulation, as a function of distance, for the same 12 frequencies discussed earlier.
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Figure 6. The total horizontal magnetic field predicted at
three locations, including (left) directly at HAARP, (middle)
150 km along the northern axis of HAARP, and (right)
150 km to the east of HAARP.
ionosphere cavity [Stubbe et al., 1982; Rietveld et al., 1989;
Cohen et al., 2012]. The decrease in efficiency with frequency is not included in the model of Barr and Stubbe
[1997], which assumed that ELF/VLF generation efficiency
is proportional to HF power density and not to a function of
ELF/VLF frequency. The model here includes the full heating and cooling physics and so the decrease in efficiency
beyond 2 kHz present in all results of Figure 6 is a result of
this effect. However, at most frequencies above 5 kHz, the
northward and southward beat wave techniques produce
stronger amplitudes than amplitude modulation, although
they also seem to exhibit more variability with frequency.
[25] The two beat wave techniques are nearly identical at
HAARP, due to the symmetry inherent from the fact that the
receiver is right at the location of the array. However, the
disparity between northward and southward beat waves is
extremely strong 150 km north of HAARP, with a difference
between the two as a high as 15 dB, similar to the geometric
modulation sawtooth sweep [Cohen et al., 2008b]. The
north-south disparity is strongest between 3 and 10 kHz,
corresponding to frequencies near where the speed of the
radiation pattern entering the ionosphere is close to the speed
of light. However, at a location 150 km to the east, the disparity between north and south beat wave techniques largely
vanishes.
4. Discussion
[26] It should be emphasized that the model we describe
here includes collisional absorption of HF heating and cooling only. At higher altitudes, >100 km, these effects disappear, as the atmosphere is thin and collisions too rare. Thus,
ELF/VLF wave generation via this technique does not efficiently occur above 100 km, because the ionosphere recovers
much more slowly than the 10 s to 100 s of ms periods in the
ELF/VLF range. The theoretical formulation for whistler
wave generation in the F-region [Kuo et al., 2011, 2012], is
thus not included in the model.
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[27] Nonetheless, the model shows that beat wave generation can be a substantially more effective technique for ELF/
VLF wave generation compared to amplitude modulation.
We do note that the beat wave approach uses 3 dB more HF
power since both halves of the array transmit at full power
(whereas for amplitude modulation the average power is half
the maximum), but even after accounting for this, beat wave
generation yields up to 10–20 dB stronger signal amplitudes
at some locations.
[28] We thus conclude that the beat wave method for ELF/
VLF wave generation generally produce more ELF/VLF
power than sinusoidal power modulation at frequencies
above 5 kHz, by virtue of the phasing effects of the signal
generation in the D-region ionosphere. An F-region source is
thus not needed to explain the results of Kuo et al. [2012],
who present higher amplitudes for beat wave compared to
amplitude modulation as evidence for an F-region source.
Given that generation in the D-region has a long and well
documented history, whereas F-region generation via beat
wave has not been demonstrated prior to these recent papers,
we conclude that an F-region source mechanism with beat
wave HF heating remains unvalidated. While we cannot rule
out the feasibility of the physical mechanism suggested by
Kuo et al. [2011, 2012], it seems clear that further experiments are required to establish the viability of the electrojetindependent beat wave generation technique.
[29] Acknowledgments. This work has been supported by ONR
award N0014-09-1-0100 and AFRL award FA9453-11-C-0011 to Stanford
University with subaward 27239350-50917-B to CU Denver. This work is
also supported by NSF grants AGS-0940248 and ANT-0944639, ONR grant
N000141010909, DARPA contract HR0011-09-C-0099, and DARPA grant
HR0011-10-1-0061 to University of Florida with subaward UF-EIES1005017-UCD to CU Denver. The experiments were conducted as part of
the SSRC summer campaign at HAARP, and we thank Ed Kennedy for organizing it. We thank Mike McCarrick and the HAARP operators for their
help.
[30] Robert Lysak thanks the reviewers for their assistance in evaluating this paper.
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